About the updates of the dropbox-client: They do push updates, but are relatively conservative about when to do so. If you always want the latest beta client, download it in their forums. Others just wait.

How does this update itself? As far as I know, the "best" place of finding recent updates of DropBox is to visit iusethis. I may be blind, but I didn't find anything in the preferences nor on the getdropbox website.

I love dropbox. I use it on 3 computers:
Macbook for home use and 2 desktops (one Ubuntu and one WinXP) at work. Keeps all my frequently needed files matched up and where I need them without ever needing to worry about them.